A stochastic level set method for Subspace Mumford-Shah based image segmentation

Abstract

Recently, the Subspace Mumford-Shah (SMS) model has been proposed for simultaneous texture segmentation and feature selection. The optimal segmentation and features are obtained via solving a joint minimization problem. Due to the non-convexity of the objective function, the computation of a solution is non-trivial and even more difficult than standard Mumford-Shah-type problems. Various ways to compute a solution have been proposed. But none of them address the problem of trapping in a local minimum from the global optimization point of view. In this paper, we propose a stochastic level set method that aims at searching for a globally optimal solution. The proposed method uses a hybrid approach which combines gradient based and stochastic optimization methods to resolve the problem of sensitivity to the initial guess. The core of the algorithm is a basin hopping scheme which uses global updates to escape from local traps in a way that is much more effective than standard stochastic methods. In our experiments, a very high quality solution is obtained within a few stochastic hops whereas the solutions obtained with pure gradient descent are incomparable even after thousands of steps.